What is the derivative of x*e^{-1/(x^2}) ?

The derivative of x*e^{-1/(x^2}) is e^{-1/(x^2)}+(2e^{-1/(x^2)})/(x^2)

What is the first derivative of x*e^{-1/(x^2}) ?

The first derivative of x*e^{-1/(x^2}) is e^{-1/(x^2)}+(2e^{-1/(x^2)})/(x^2)

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\frac{d}{d x} (x \cdot e^{- \frac{1}{x ^{2}}})

e^{- \frac{1}{x ^{2}}} + \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{2}}

Solution steps

\frac{d}{d x} (x e^{- \frac{1}{x ^{2}}})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{- \frac{1}{x ^{2}}}

= \frac{d x}{d x} e^{- \frac{1}{x ^{2}}} + \frac{d}{d x} (e^{- \frac{1}{x ^{2}}}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{- \frac{1}{x ^{2}}}) = \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{3}}

= 1 \cdot e^{- \frac{1}{x ^{2}}} + \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{3}} x

Simplify

1 \cdot e^{- \frac{1}{x ^{2}}} + \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{3}} x : e^{- \frac{1}{x ^{2}}} + \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{2}}

= e^{- \frac{1}{x ^{2}}} + \frac{2 e ^{- \frac{1}{x ^{2}}}}{x ^{2}}

(e^{- 5 x})^{^{'}}

\int \frac{x + 4}{x} d x

\frac{d}{d x} (a x^{3} ln (\frac{x}{4}) + b x^{2} (x - 4))

ln (3 x^{5})

\frac{d}{d x} (\frac{e ^{x}}{4 - 2 x})

What is the derivative of x*e^{-1/(x^2}) ?
The derivative of x*e^{-1/(x^2}) is e^{-1/(x^2)}+(2e^{-1/(x^2)})/(x^2)
What is the first derivative of x*e^{-1/(x^2}) ?
The first derivative of x*e^{-1/(x^2}) is e^{-1/(x^2)}+(2e^{-1/(x^2)})/(x^2)